Addendum: Non-Fermi-liquid behavior ind- andf-electron metals

Abstract

A relatively new class of materials has been found in which the basic assumption of Landau Fermi-liquid theory-that at low energies the electrons in a metal should behave essentially as a collection of weakly interacting particles-is violated. These ''non-Fermi-liquid'' systems exhibit unusual temperature dependences in their low-temperature properties, including several examples in which the specific heat divided by temperature shows a singular log T temperature dependence over more than two orders of magnitude, from the lowest measured temperatures in the milliKelvin regime to temperatures over 10 K. These anomalous properties, with their often pure power-law or logarithmic temperature dependences over broad temperature ranges and inherent low characteristic energies, have attracted active theoretical interest from the first experimental report in 1991. This article first describes the various theoretical approaches to trying to understand the source of strong temperature-and frequency-dependent electron-electron interactions in non-Fermi-liquid systems. It then discusses the current experimental body of knowledge, including a compilation of data on non-Fermi-liquid behavior in over 50 systems. The disparate data reveal some interesting correlations and trends and serve to point up a number of areas where further theoretical and experimental work is needed. CONTENTS I. Introduction 798 II. Theory 799 A. The single-impurity multichannel Kondo model and non-Fermi liquids 799 B. Quantum critical point theories 800 1. Scaling analysis at a quantum critical point 801 2. Spin-fluctuation theory of non-Fermi-liquid behavior 802 a. Millis and Hertz 802 b. Self-consistent renormalization model 802 3. Local deviation from Fermi-liquid behavior 804 C. Disorder-induced non-Fermi-liquid behavior theories 804 III. Experiment 806 A. Doped systems 807 1. Antiferromagnetism ''distant'' in the phase diagram 807 a. U x Y 1Ϫx Pd 3 (I) 808 b. UCu 5Ϫx Pd x (I) 820 c. UCu 5Ϫx Pt x (II) 822 d. UCu 4 Ni (II) 823 e. UCu 5Ϫx Al x (III) 823 f. Ce 1Ϫx La x Cu 2 Si 2 (I) 824 g. (U x La 1Ϫx) 2 Zn 17 (I) 824 h. U 2 Cu 17Ϫx Al x (I) 825 i. U 1Ϫx Y x Al 2 (I) 825 j. U x Th 1Ϫx Ru 2 Si 2 , xр0.07 (I) 826 k. U x Y 1Ϫx Ru 2 Si 2 , xр0.07 (III) 826 l. U x Th 1Ϫx Pt 2 Si 2 , xр0.07 (III) 826 m. U x Th 1Ϫx Pd 2 Si 2 (I?) 826 n. U 1Ϫx M x Pt 3 (I) 827 o. Ce 1Ϫx Th x RhSb (I?) 827 p. URu 2Ϫx Re x Si 2 (III) 827 q. U 2 Pd 1Ϫx Si 3ϩx (II) 828 r. Ce 0.1 La 0.9 Pd 2 Al 3 (III) 828 s. U 0.1 M 0.9 In 3 , MϭY,Pr,La (I) 828 t. CePt 0.96 Si 1.04 (I?) 828

Non-Fermi Liquid Regimes and Superconductivity in the Low Temperature Phase Diagrams of Strongly Correlated d- and f-Electron Materials

“…This is in agreement with mean-field theory of superconductivity for nearly antiferromagnetic metals which demonstrates that magnetically mediated superconductivity is more stable in quasi-2D compared to 3D [134]. Monthoux et al [134], however, emphasize that this kind of magnetically mediated superconductivity is sensitive to small changes in the band structure, possibly yielding an explanation why CeRhIn 5 with a c/a ratio intermediate between CeIrIn 5 and CeCoIn 5 only exhibits superconductivity below T c = 110 mK. For the entire series of CeT In 5 compounds, both the specific heat [135] and the spin-lattice relaxation rate divided by temperature 1/T 1 T , measured by means of NQR [136][137][138], provide compelling evidence for the existence of line nodes in the superconducting energy gap and therefore unconventional superconductivity.…”

“…The NFL characteristics included a linear T -dependence of ρ, a logarithmic in T divergence of C/T , and a non-Curie Weiss χ that varies as T 1/2 . Interestingly, these NFL signatures were later observed in many other d-and f -electron systems [1,2,4,5], including both chemically substituted and stoichiometric compounds. The low temperature-composition (T -x) phase diagram of the Y 1−x U x Pd 3 system is shown in Fig.…”

“…A large number of strongly correlated d-and f -electron systems have been investigated during the past two decades in which the Fermi liquid paradigm appears to be violated [1][2][3][4][5]. These systems are based on certain intermetallic compounds containing transition metal, lanthanide, or actinide ions such as Mn, Fe, Ce, Pr, Sm, Eu, Yb and U with partially-filled d-or f -electron shells in which the localized d-or f -states are hybridized with conduction electron states.…”

Suppression of ferromagnetism in the La(VxCr1−x)Sb3system

“…The effective moment also decreases as x increases, but in a more subtle way. Instead of quickly approaching to zero as seen in the suppression of ferromagnetism in the itinerant ferromagnets [1][2][3][4], µ eff per Cr varies slightly as x increases, from 3.9 µ B for x = 0 to 2.9 µ eff for x = 0.88. Whereas the former value is close to the theoretical effective moment of Cr 3+ , the latter one is close to Cr 4+ .…”

“…The suppression of an itinerant ferromagnetic transition temperature to zero is of specific interest, since it may lead to the discovery of a quantum critical point (QCP) [1][2][3][4][5][6] which exhibits exotic physical properties, such as non-Fermi liquid behavior and even superconductivity. The Stoner model has been developed to describe a mechanism of an itinerant ferromagnetic system, and is based on the premise that the magnetic properties of the itinerant ferromagnets originate from de-localized electrons [7].…”